298
Richard C. Zimmerman and Arnold G. Dekker
Fig. 2. Definitions of radiance and angular orientation at a point in space (after Kirk, 1994). L(θ, φ) is the radiance incident on area
dA at zenith angle θ and azimuth angle φ, given the radiant flux into the small solid angle dω. The Cosine Law is illustrated by the
relationship between the area of illumination normal to dω, defined by dA, and the surface-normalized area of illumination,
dA
cos θ
.
flux is absorbed within the medium ( a ), some is
scattered out of the beam ( s ), and some is transmitted unaltered through the medium ( t ). The beam
absorptance (A) represents the fraction of the incident radiant flux absorbed by the medium:
A ≡
a
i
(4)
Fig. 3. Interaction of a beam of light with a thin optically active
layer. The flux incident ( i ) on the medium of thickness r is
dissipated by scattering out of the path ( s ) and by absorption
( a ) within the medium. The remaining flux ( t ) is transmitted
out of the medium.
The beam scatterance (B) is the fraction of incident
radiant flux scattered out of the beam:
B ≡
s
i
(5)
Finally, the beam transmittance (T ) is the fraction
emerging from the medium:
T ≡
t
i
(6)
It thus follows that A + B + T = 1 because these
terms represent dimensionless ratios normalized to
the incident flux. In hydrologic optics, the absorption and scattering coefficients have dimensions of
inverse meters (i.e. m
−1 ). Thus, the beam absorption
and scattering coefficients are defined as the depth
derivatives of the absorptance and scatterance over
an infinitesimally small distance (r ):
a ≡ lim
r →0
A
r
(7)
b ≡ lim
r →0
B
r
(8)
Beam attenuation is defined by summing the absorption and scattering coefficients:
c ≡ a + b
(9)
If we assume B = 0, as in the case of a transparent
chemical solution subjected to spectrophotometric
Richard C. Zimmerman and Arnold G. Dekker
Fig. 2. Definitions of radiance and angular orientation at a point in space (after Kirk, 1994). L(θ, φ) is the radiance incident on area
dA at zenith angle θ and azimuth angle φ, given the radiant flux into the small solid angle dω. The Cosine Law is illustrated by the
relationship between the area of illumination normal to dω, defined by dA, and the surface-normalized area of illumination,
dA
cos θ
.
flux is absorbed within the medium ( a ), some is
scattered out of the beam ( s ), and some is transmitted unaltered through the medium ( t ). The beam
absorptance (A) represents the fraction of the incident radiant flux absorbed by the medium:
A ≡
a
i
(4)
Fig. 3. Interaction of a beam of light with a thin optically active
layer. The flux incident ( i ) on the medium of thickness r is
dissipated by scattering out of the path ( s ) and by absorption
( a ) within the medium. The remaining flux ( t ) is transmitted
out of the medium.
The beam scatterance (B) is the fraction of incident
radiant flux scattered out of the beam:
B ≡
s
i
(5)
Finally, the beam transmittance (T ) is the fraction
emerging from the medium:
T ≡
t
i
(6)
It thus follows that A + B + T = 1 because these
terms represent dimensionless ratios normalized to
the incident flux. In hydrologic optics, the absorption and scattering coefficients have dimensions of
inverse meters (i.e. m
−1 ). Thus, the beam absorption
and scattering coefficients are defined as the depth
derivatives of the absorptance and scatterance over
an infinitesimally small distance (r ):
a ≡ lim
r →0
A
r
(7)
b ≡ lim
r →0
B
r
(8)
Beam attenuation is defined by summing the absorption and scattering coefficients:
c ≡ a + b
(9)
If we assume B = 0, as in the case of a transparent
chemical solution subjected to spectrophotometric